Chemistry and Measurements

Write the equality and two conversion factors for each of the following pairs of units:

(a) centimeters and inches

(b) kilometers and miles

(c) pounds and grams

(d) quarts and liters

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following:
a. A bee flies at an average speed of $3.5m$ per second.
b. The Daily Value (DV) for potassium is $3.5g$.
c. An automobile traveled $2.60km$ on $1L$ of gasoline.
d. Silicon makes up $28.2\%$ by mass of Earth's crust.

Write the equality and two conversion factors for each of the following pairs of units:

a. centimeters and meters

b. nanograms and grams

c. liters and kiloliters

d. seconds and milliseconds

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following:
a. The Daily Value (DV) for iodine is $150 mcg$
b. Gold jewelry contains $58\%$ gold by mass.
c. The price of a liter of milk is $\$1.65$
d. A metric ton is $1000kg$

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following:

a. One yard is $3 ft.$

b. One kilogram is $2.20 lb$

c. A car goes $27 mi$ on $1 gal$ of gas .

d. Sterling silver is $93\%$ silver by mass.

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following:

a. One liter is $1.06 qt$

b. At the store, oranges are $\$1.29$per $lb$

c. One deciliter contains $100 mL$

d. An $18$ -carat gold ring contains $75\%$ gold by mass.

Perform each of the following conversions using metric conversion factors: 

a. $44.2$ mL to liters 

b. $8.65$m to nanometers 

c. $5.2 \times {10}^8$g to megagrams 

d. $0.72$ Ks to milliseconds

Perform each of the following conversions using metric conversion factors: 

a. $4.82 \times {10}^{-5}$ L to picoliters 

b. $575.2$ dm to kilometers 

c. $5 \times {10}^{-4}$ kg to micrograms 

d. $6.4 \times {10}^{10}$ ps to seconds 

Perform each of the following conversions using metric and U.S. conversion factors: 

a. 3.428 lb to kilograms 

b. 1.6 m to inches 

c. 4.2 L to quarts 

d. 0.672 ft to millimeters 

Perform each of the following conversions using metric and U.S. conversion factors: 

a. 0.21 lb to grams 

b. 11.6 in. to centimeters 

c. 0.15 qt to milliliters 

d. 35.41 kg to pounds 

Use metric conversion factors to solve each of the following problems: 

a.If a student is 175 cm tall, how tall is the student in meters? 

b. A cooler has a volume of 5000 mL. What is the capacity of the cooler in liters? 

c. A hummingbird has a mass of 0.0055 kg. What is the mass, in grams, of the hummingbird? 

d. A balloon has a volume of 3500 cm³. What is the volume in liters?

Use metric conversion factors to solve each of the following problems: 

a. The Daily Value (DV) for phosphorus is 800 mg. How many grams of phosphorus are recommended? 

b. A glass of orange juice contains 3.2 dL of juice. How many milliliters of orange juice are in the glass? 

c. A package of chocolate instant pudding contains 2840 mg of sodium. How many grams of sodium are in the pudding? 

d. A jar contains 0.29 kg of olives. How many grams of olives are in the jar? 

 Solve each of the following problems using one or more conversion factors: 

a. A container holds 0.500 qt of liquid. How many milliliters of lemonade will it hold? 

b. What is the mass, in kilograms, of a person who weighs 175 lb? 

c. An athlete has 15% body fat by mass. What is the weight of fat, in pounds, of a 74-kg athlete? 

d. A plant fertilizer contains 15% nitrogen (N) by mass. In a container of soluble plant food, there are 10.0 oz of fertilizer. How many grams of nitrogen are in the container? 

Using conversion factors, solve each of the following clinical problems:

a. A nurse practitioner prepares an injection of promethazine, an antihistamine used to treat allergic rhinitis. If the stock bottle is labeled $25 \mathrm{mg}/\mathrm{mL}$ and the order is a dose of data-custom-editor="chemistry" $12.5 \mathrm{mg}$, how many milliliters will the nurse draw up in the syringe?

b. You are to give ampicillin data-custom-editor="chemistry" $25 \mathrm{mg}/\mathrm{kg}$ to a child with a mass of data-custom-editor="chemistry" $67 \mathrm{lb}$. If stock on hand is data-custom-editor="chemistry" $250 \mathrm{mg}/\mathrm{capsule}$, how many capsules should be given?

Using conversion factors, solve each of the following clinical problems:

a. A nurse practitioner prepares $500. \mathrm{mL}$ of an IV of normal saline solution to be delivered at a rate of $80. \mathrm{mL}/\mathrm{h}$. What is the infusion time, in hours, to deliver $500. \mathrm{mL}$?

b. A nurse practitioner orders Medrol to be given $1.5 \mathrm{mg}/\mathrm{kg}$ of body weight. Medrol is an anti-inflammatory administered as an intramuscular injection. If a child weighs $72.6 \mathrm{lb}$ and the available stock of Medrol is $20. \mathrm{mg}/\mathrm{mL}$, how many milliliters does the nurse administer to the child?

Using conversion factors, solve each of the following clinical problems:

a. You have used $250 \mathrm{L}$ of distilled water for a dialysis patient. How many gallons of water is that? 

b. A patient needs $0.024 \mathrm{g}$ of a sulfa drug. There are $8-\mathrm{mg}$ tablets in stock. How many tablets should be given?

c. The daily dose of ampicillin for the treatment of an ear infection is $115 \mathrm{mg}/\mathrm{kg}$ of body weight. What is the daily dose for a $34-\mathrm{lb}$ child?

d. You need $4.0 \mathrm{oz}$ of a steroid ointment. How many grams of ointment does the pharmacist need to prepare?

Solve each of the following problems using one or more conversion factors: 

a. Wine is $12\%$ alcohol by volume. How many milliliters of alcohol are in a $0.750-\mathrm{L}$ bottle of wine?

b. Blueberry high-fiber muffins contain $51\%$ dietary fiber by mass. If a package with a net weight of $12 \mathrm{oz}$ contains six muffins, how many grams of fiber are in each muffin?

c. A jar of crunchy peanut butter contains $1.43 \mathrm{kg}$ of peanut butter. If you use $8.0\%$ of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container?

d. In a candy factory, the nutty chocolate bars contain $22.0\%$ pecans by mass. If $5.0 \mathrm{kg}$ of pecans were used for candy last Tuesday, how many pounds of nutty chocolate bars were made?

Using conversion factors, solve each of the following clinical problems:

a. The physician has ordered $1.0 \mathrm{g}$ of tetracycline to be given every six hours to a patient. If your stock on hand is $500-\mathrm{mg}$ tablets, how many will you need for one day's treatment?

b. An intramuscular medication is given at $5.00 \mathrm{mg}/\mathrm{kg}$ of body weight. What is the dose for a $180-\mathrm{lb}$ patient?

c. A physician has ordered $0.50 \mathrm{mg}$ of atropine, intramuscularly. If atropine were available as $0.10 \mathrm{mg}/\mathrm{mL}$ of solution, how many milliliters would you need to give?

d. During surgery, a patient receives $5.0 \mathrm{pt}$ of plasma. How many milliliters of plasma were given?

Determine the density (g/mL) for each of the following: 

a. A 20.0-mL sample of a salt solution has a mass of 24.0 g. 

b. A cube of butter weighs 0.250 lb and has a volume of 130.3 mL. 

c. A gem has a mass of 4.50 g. When the gem is placed in a graduated cylinder containing 12.00 mL of water, the water level rises to 13.45 mL. 

d. A 3.00-ml sample of medication has a mass of 3.85 g. 

What is the density (g/mL) of each of the following samples? 

a. A lightweight head on a golf club is made of titanium. The volume of a sample of titanium is 114 cm³ and the mass is 514.1 g. 

b. A syrup is added to an empty container with a mass of 115.25 g. When 0.100 pt of syrup is added, the total mass of the container and syrup is 182.48 g. 

c. A block of aluminum metal has a volume of 3.15 L and a mass of 8.51 kg.

Use the density values in Table 2.8 to solve each of the following problems: 

a. A graduated cylinder contains 18.0 mL of water. What is the new water level, in milliliters, after 35.6 g of silver metal is submerged in the water? 

b. A thermometer containing 8.3 g of mercury has broken. What volume, in milliliters, of mercury spilled? 

c. A fish tank holds 35 gal of water. How many kilograms of water are in the fish tank? 

Determine the density (g/mL) for each of the following: 

a. The fluid in a car battery has a volume of 125 mL and a mass of 155 g. 

b. A plastic material weighs 2.68 lb and has a volume of 3.5 L. 

c. A 4.000-mL urine sample from a person suffering from diabetes mellitus has a mass of 4.004 g. 

d. A solid object has a mass of 1.65 lb and a volume of 170 mL.

What is the density (g/mL) of each of the following samples? 

a. An ebony carving has a mass of 275 g and a volume of 207 cm³.

b. A 14.3-cm³ sample of tin has a mass of 0.104 kg. 

C. A bottle of acetone (fingernail polish remover) contains 55.0 mL of acetone with a mass of 43.5 g.

Use the density values in Table 2.8 to solve each of the following problems: 

a. How many liters of ethanol contains 1.50 kg of ethanol? 

b. How many grams of mercury are present in a barometer that holds 6.5 mL of mercury? 

c. A sculptor has prepared a mold for casting a silver figure. The figure has a volume of 225 cm³. How many ounces of silver are needed in the preparation of the silver figure?

Use the density values in Table 2.8 to solve each of the following problems:

a. What is the mass, in grams, of a cube of copper that has a volume of 74.1 cm³? 

b. How many kilograms of gasoline fill a 12.0-gal gas tank? 

c. What is the volume, in cubic centimeters, of an ice cube that has a mass of 27 g?

In an old trunk, you find a piece of metal that you think may be aluminum, silver, or lead. You take it to a lab, where you find it has a mass of 217 g and a volume of 19.2 cm³. Using Table 2.8, what is the metal you found?

Use the density values in Table 2.8 to solve each of the following problems: 

a. If a bottle of olive oil contains 1.2 kg of olive oil, what is the volume, in milliliters, of the olive oil? 

b. A cannon ball made of iron has a volume of 115 cm³. What is the mass, in kilograms, of the cannon ball? 

c. A balloon filled with helium has a volume of 7.3 L. What is the mass, in grams, of helium in the balloon?

Solve each of the following problems: 

a. A urine sample has a density of 1.030 g/mL. What is the specific gravity of the sample? 

b. A 20.0-ml sample of a glucose IV solution has a mass of 20.6 g. What is the density of the glucose solution? 

c. The specific gravity of vegetable oil is 0.92. What is the mass, in grams, of 750 mL of vegetable oil? 

d. A bottle containing 325 g of cleaning solution is used to clean hospital equipment. If the cleaning solution has a specific gravity of 0.850, what volume, in milliliters, of solution was used?

a. Write an equality and two conversion factors for Greg's serum iron level. 

b. How many micrograms of iron were in the 8.0-ml Sample of Greg's blood?

a. Write an equality and two conversion factors for one tablet of the iron supplement. 

b. How many grams of iron will Greg consume in one week? 

Each tablet contains 65 mg of iron, which is given for iron supplementation. 

Solve each of the following problems: 

a. A glucose solution has a density of 1.02 g/mL. What is its specific gravity? 

b. A 0.200 mL sample of very-low-density lipoprotein (VLDL) has a mass of 190 mg. What is the density of the VLDL? 

c. Butter has a specific gravity of 0.86. What is the mass, in grams, of 2.15 L of butter? 

d. A 5.000-mL urine sample has a mass of 5.025 g. If the normal range for the specific gravity of urine is 1.003 to 1.030, would the specific gravity of this urine sample indicate that the patient could have type 2 diabetes? 

Suppose you have two 100-mL graduated cylinders. In each cylinder, there is 40.0 mL of water. You also have two cubes: one is lead, and the other is aluminum.

Suppose you have two$100 ml$ graduated cylinders. In each cylinder, there is $40 ml$ of water. You also have two cubes: one is lead, and the other is aluminum. Each cube measures $2 cm$on each side. After you carefully lower each cube into the water of its own cylinder, what will the new water level be in each of the cylinders?

State the temperature on the Celsius thermometer to the correct number of significant figures: (2.3)

State the temperature on the Celsius thermometer to the correct number of significant figures: (2.3)

In which of the following pairs do both numbers contain the same number of significant figures? $(2.2)$

a. $2.0500 \mathrm{m} and 0.0205 \mathrm{m}$

b. $600.0 \mathrm{K} \mathrm{and} 60 \mathrm{K}$

c. $0.00075 \mathrm{s} \mathrm{and} 75000 \mathrm{s}$

d. $6.240 \mathrm{L} \mathrm{and} 6.240\times {10}^{-2} \mathrm{L}$

In which of the following pairs do both numbers contain the same number of significant figures? $(2.2)$

a. $3.44\times {10}^{-1}\mathrm{g} and 0.0344 \mathrm{g}$

b. $0.0098 \mathrm{s} and 9.8\times {10}^4 \mathrm{s}$

c. $6.8\times {10}^3 \mathrm{m} and 68000 \mathrm{m}$

d. $2.58 .000 \mathrm{g} and 2.58\times {10}^{-2} \mathrm{g}$

Indicate if each of the following is answered with an exact number or a measured number: (2.2)

a. number of legs

b. height of table

c. number of chairs at thetable

d. area of tabletop

Measure the length of each of the objects in diagrams (a), (b). and (c) using the metric ruler in the figure. Indicate the number of significant figures for each and the estimated digit for each. (2.2)

The length of this rug is $38.4 in$,and the width is $24.2$  in.($2.3,2.6$)

a. What is the length of this rug, in centimeters?

b. What is the width of this rug, in centimeters?

c. How many significant figures are in the length measurement?

d. Calculate the area of the rug, in square centimeters, to the correct number of significant figures, $Area=(Length\times Width)$

Each of the following diagrams represents a container of water and a cube. Some cubes float while others sink. Match diagrams $1. 2, 3, or 4$ with one of the following descriptions and explain your choices: $(2.7)$

a. The cube has a greater density than water.

b. The cube has a density that is $0.80 \mathrm{g}/\mathrm{mL}$.

c. The cube has a density that is one-half the density of water.

d. The cube has the same density as water.

What is the density of the solid object that is weighed and submerged in the water 

Consider the following solids, The solids $A, B, and C$ represent aluminum $(D=2.70 \mathrm{g}/\mathrm{mL})$, gold )), and silver $(\mathrm{D}=10.5 \mathrm{g}/\mathrm{mL})$. If each has a mass of $10.0 \mathrm{g}$, what is the identity of each solid? (2.7)

A graduated cylinder contains three liquids $A. B, and C$, which have different densities and do not mix: mercury $(D=13.6 g / mL)$. vegetable oil $(D=0.92 g / mL)$, and water $(D=1,00 g/mL)$. Identify the liquids $A,B and C$ in the cylinder. (2.7)

The gray cube has a density of $4.5 g/c{m}^3$ . Is the density of the green cube the same, lower than, or higher than that of the gray cube? (2.7)

A shipping box has a length of 7.00 in., a width of 6.00 in., and a height of 4.00 in. (2.3,2.6)

a. What is the length of the box, in centimeters?

b. What is the width of the box, in centimeters?

c. How many significant figures are in the width measurement?

d. Calculate the volume of the box, in cubic centimeters, to the correct number of significant figures.

The grey cube has a density of $4.5 g/c{m}^3$ . Is the density of the green cube the same, lower than, or higher than that of the grey cube? (2.7)

Round off or add zeros to the following calculated answers to give a final answer with three significant figures: (2.2)

a. $0.00001258 \mathrm{L}$

b. $3.528\times {10}^2 \mathrm{kg}$

c. $125111 \mathrm{m}$

d. $34.9673 \mathrm{s}$

Round off or add zeros to the following calculated answers to give a final answer with three significant figures: (2.2)

a. $58.703 \mathrm{mL}$

b. $3\times {10}^{-3}s$

c. $0.010826 \mathrm{g}$

d. $1,7484\times {10}^3 \mathrm{ms}$

A dessert contains $137.25 \mathrm{g}$ of vanilla ice cream. $84 \mathrm{g}$ of fudge sauce, and $43.7 \mathrm{g}$ of nuts.

a. What is the total mass, in grams, of the dessert?

b. What is the total weight, in pounds, of the dessert?